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State whether the following equation has a solution or not? 3 sin θ = 5

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Question

State whether the following equation has a solution or not?

3 sin θ = 5

Sum
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Solution

3 sin θ = 5

Dividing both sides by 3: `sintheta = 5/3`

The value of sin⁡θ always lies between −1 and +1 for real angles.

But here, sin⁡θ = `5/3` ≈ 1.666, which is greater than 1.

Since sin⁡θ cannot be greater than 1

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Chapter 3: Trigonometric Functions - Miscellaneous exercise 3 [Page 109]

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Balbharati Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
Chapter 3 Trigonometric Functions
Miscellaneous exercise 3 | Q 3.4 | Page 109

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